Worrall, who began his career at Gigg Lane, netted a free kick 16 minutes from time to take Southend above Bury in the League Two table.
Nathan Cameron should have done better with a close-range header, while Tutte missed the target on two more occasions as Bury continued to push for the opening goal of the match.
Southend had barely registered a threat in the final third, but they did enough to frustrate the hosts for the remainder of the half.
Soon after the restart, Joe Riley curled a free kick wide for the home side, before substitute Worrall finally made Bury stopper Nick Pope work with a free kick, but it was comfortably dealt with by the on-loan Charlton Athletic goalkeeper.
However, in the 74th minute, Worrall took his second chance from a set piece, curling the ball over the wall and into the top corner for his sixth goal of the campaign.
Bury pushed for an equaliser but they couldn't break down a resilient Southend defence as the visitors registered their 12th away success of the season.